JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Atomic Structure

Values of work function

(W_{0})

for a few metals are given below

Metal	Li	Na	K	Mg	Cu	Ag
$W_{0} / eV$	2.42	2.3	2.25	3.7	4.8	4.3

The number of metals which will show photoelectric effect when light of wavelength 400 nm falls on it is ______

Given:

h = 6.6 \times 1 0^{- 34} J s

c = 3 \times 1 0^{8} m s^{- 1}

e = 1.6 \times 1 0^{- 19} C

Answer: 3

Solution

The energy of a

400 nm

photon is

E = \frac{h c}{λ} = \frac{6.6 \times 1 0 ^{- 34} \times 3 \times 1 0 ^{8}}{400 \times 1 0 ^{- 9}} = 4.95 \times 1 0^{- 19} J = 3.09 eV

The photoelectric effect occurs only when this energy is at least the work function. Lithium (

2.42 eV

), sodium (

2.30 eV

) and potassium (

2.25 eV

) have work functions below

3.09 eV

, while magnesium, copper and silver do not. The number of metals that show the photoelectric effect is 3.

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Integer answer